BR112020012033A2 - transformation-based image encoding method and device for the same - Google Patents

Abstract

It is an image decoding method carried out by means of a decoding device according to the present invention, comprising the steps of: deriving quantized transform coefficients in relation to a target block from a bit stream; perform an inverse quantization in relation to the transform coefficients quantized in relation to the target block and derive transform coefficients; derive residual samples in relation to the target block based on the reduced inverse transform in relation to the transform coefficients; and generate a reconstructed figure based on the residual samples in relation to the target block and prediction samples in relation to the target block. The reduced inverse transform is performed based on a reduced reverse transform matrix. The reduced inverse transform matrix is a non-square matrix whose number of columns is less than the number of rows.

Description

“IMAGE CODING METHOD BASED ON TRANSFORMATION AND DEVICE FOR THE SAME” REVELATION FUNDAMENTALS REVELATION FIELD

[001] The present disclosure relates to an image encoding technology, and, more particularly, to an image encoding method and apparatus based on the transform of an image encoding system.

RELATED TECHNIQUE

[002] Demands for high resolution and high quality images, such as HD (High Definition) images and UHD (Ultra High Definition) images have increased in several fields. Since image data has high resolution and high quality, the amount of information or bits to be transmitted increases in relation to legacy image data. Correspondingly, when image data is transmitted using a medium such as a conventional wired / wireless broadband line or image data is stored using an existing storage medium, transmission costs and storage costs are increased.

[003] Correspondingly, there is a need for a highly efficient image compression technique to effectively transmit, store and reproduce high resolution and high quality image information.

SUMMARY

[004] An objective of the present disclosure is to provide a method and an apparatus to enhance the efficiency of image coding.

[005] Another objective of the present disclosure is to provide a method and an apparatus to enhance the transform efficiency.

[006] Yet another objective of the present disclosure is to provide a method and an apparatus for enhancing the efficiency of a residual encoding through a transform.

[007] Yet another objective of the present disclosure is to provide an image encoding method and apparatus based on a reduced transform.

[008] An exemplary embodiment of the present disclosure provides an image decoding method performed by a decoding device. The method includes: deriving quantized transform coefficients for a target block from a bit stream, deriving transform coefficients by performing a decanting for the quantized transform coefficients for the target block, deriving residual samples for the target block based in the reduced inverse transform for the transform coefficients, and generate a reconstructed figure based on the residual samples for the target block and prediction samples for the target block, and the reduced inverse transform is performed based on a reduced reverse transform matrix, and the reduced inverse transform matrix is a non-square matrix, the number of columns in the non-square matrix being less than the number of rows in the non-square matrix.

[009] Another exemplary embodiment of the present disclosure provides an image encoding method performed by an encoding apparatus. The method includes: deriving residual samples for a target block, deriving transform coefficients for the target block based on the reduced transform for residual samples, deriving quantized transform coefficients by performing a quantization based on the transform coefficients for the target block , and encode information about the quantized transform coefficients, and the reduced transform is performed based on a reduced transform matrix, and the reduced transform matrix is a non-square matrix, the number of rows of the non-square matrix being less than the number of columns in the non-square matrix.

[010] Yet another exemplary embodiment of the present disclosure provides a decoding apparatus for performing an image decoding. The decoding apparatus includes: an entropy decoder that derives quantized transform coefficients for a target block from a bit stream, a decantant that derives transform coefficients by performing a decanting for the quantized transform coefficients for the target block , an inverse transformer that derives residual samples for the target block based on the reduced reverse transform for the transform coefficients, and an adder that generates a reconstructed figure based on the residual samples for the target block and prediction samples for the target block, and the reduced inverse transform is performed based on a reduced inverse transform matrix, and the reduced inverse transform matrix is a non-square matrix, the number of rows in the non-square matrix being less than the number of columns in the non-square matrix. square.

[011] Yet another exemplary embodiment of the present disclosure provides an encoding apparatus for performing image encoding. The coding apparatus includes: a subtractor that derives residual samples for a target block, a transformer that derives transform coefficients for the target block based on the reduced transform for residual samples, a quantizer that derives quantized transform coefficients by performing a quantization based on the transform coefficients for the target block, and an entropy encoder that encodes information about the quantized transform coefficients, and the reduced transform is performed by a reduced transform matrix, and the reduced transform matrix is a non-matrix square, the number of rows in the non-square matrix being less than the number of columns in the non-square matrix.

[012] According to the present disclosure, it is possible to accentuate the overall image / video compression efficiency.

[013] According to the present disclosure, it is possible to reduce the amount of data to be transmitted for the residual processing through an efficient transform, and to accentuate the residual coding efficiency.

[014] According to the present disclosure, it is possible to concentrate non-zero transform coefficients in the low frequency component through the secondary transform in the frequency domain.

[015] According to the present disclosure, it is possible to carry out an image coding based on the reduced transform, thus enhancing the image coding efficiency.

BRIEF DESCRIPTION OF THE DRAWINGS

[016] Figure 1 is a schematic diagram illustrating a configuration of an image / video encoding device to which the present disclosure is applicable.

[017] Figure 2 is a schematic diagram illustrating a configuration of a video / image decoding device to which the present disclosure is applicable.

[018] Figure 3 is a schematic diagram that illustrates a multiple transform technique according to an exemplary modality.

[019] Figure 4 is a diagram that illustrates 65 intradirectional modes of prediction directions in an exemplary way.

[020] Figures 5A to 5C are flowcharts that illustrate a non-separable secondary transformation process according to an exemplary modality.

[021] Figure 6 is a diagram to explain a reduced transform according to an exemplary embodiment of the present disclosure.

[022] Figure 7 is a flowchart that illustrates a reduced transform process according to an exemplary embodiment of the present disclosure.

[023] Figure 8 is a flow chart that illustrates a reduced transformation process according to another exemplary embodiment of the present disclosure.

[024] Figure 9 is a flowchart illustrating a reduced transform process based on the non-separable secondary transform according to an exemplary embodiment of the present disclosure.

[025] Figure 10 is a diagram that illustrates a block to which the reduced transform according to an exemplary embodiment of the present disclosure is applied.

[026] Figure 11 is a flow chart illustrating an operation of a video encoding device according to an exemplary embodiment of the present disclosure.

[027] Figure 12 is a flow chart illustrating an operation of a video decoding device according to an exemplary embodiment of the present disclosure.

DESCRIPTION OF EXAMPLE MODES

[028] The present disclosure can be modified in several ways, and specific details of it will be described and illustrated in the drawings. However, the arrangements are not intended to limit disclosure. The terms used in the following description are used merely to describe specific modalities, but are not intended to limit disclosure. An expression of a singular number includes an expression of the number in the plural, as long as it is clearly read differently. The terms such as "include" and "have" are intended to indicate that the resources, numbers, steps, operations, elements, components, or combinations of them used in the following description exist and it should be understood that the possibility of existence or addition of one or more different resources, numbers, steps, operations, elements, components, or combinations thereof is not excluded.

[029] However, elements described in the disclosure are designed independently for the purpose of convenience for explaining different specific functions, and it does not mean that the elements are incorporated by independent hardware or independent software. For example, two or more elements of the elements can be combined to form a single element, or an element can be divided into plural elements. The modalities in which the elements are combined and / or divided belong to the revelation without departing from the concept of the revelation.

[030] The following description can be applied in the field of the technique that deals with videos, pictures or images. For example, an exemplary method or modality revealed in the following description can be associated with the revealed content of a Versatile Video Encoding (VVC) standard (ITU-T Rec. H.266), a video / image encoding standard next generation after VVC, or standards before the VVC standard (for example, a High Efficiency Video Coding (HEVC) standard (ITU-T Rec. H.265) or similar).

[031] Hereafter, examples of the present modality will be described in detail with reference to the attached drawings. In addition, similar numerical references are used to indicate similar elements throughout the drawings, and the same descriptions on similar elements will be omitted.

[032] In the present revelation, a video can mean a set of a series of images according to a passage of time. In general, a figuration means a unit that represents an image at a specific time, a slice is a unit that forms a part of the figuration. A picture can consist of several slices, and the terms of a picture and a slice can be mixed together as the occasion demands.

[033] A pixel or a skin can mean a minimum unit that constitutes a figuration (or image). In addition, a “sample” can be used as a term corresponding to a pixel. The sample can generally represent a pixel or a pixel value, it can represent only one pixel (a pixel value) of a luma component, and it can represent only one pixel (a pixel value) of a luma component. chroma.

[034] One unit indicates a basic image processing unit. The unit can include at least one specific area and information about the area.

Optionally, the unit can be mixed with terms such as a block, an area, or the like. In a typical case, an MxN block can represent a set of samples or transform coefficients arranged in M columns and N rows.

[035] Figure 1 briefly illustrates a structure of a video / image encoding device to which the present disclosure is applicable. Hereinafter, an encoding apparatus may include a video encoding apparatus and / or an image encoding apparatus, and the video encoding apparatus may be used as a concept comprising the image encoding apparatus.

[036] With reference to Figure 1, a video encoding apparatus 100 may include a figuration partitioner 105, a predictor 110, a residual processor 120, an entropy encoder 130, an adder 140, a filter 150 and a memory 160 Residual processor 120 may include a subtractor 121, a transformer 122, a quantizer 123, a rearranger 124, a decantant 125, an inverse transformer 126.

[037] The figuration partitioner 105 can divide an input figuration into at least one processing unit.

[038] In one example, the processing unit can be referred to as a coding unit (CU). In this case, the coding unit can be recursively divided from the largest coding unit (LCU) according to a binary and quadratic tree structure (QTBT). For example, a coding unit can be divided into a plurality of coding units of greater depth based on a quadratic tree structure, a binary tree structure and / or a tertiary tree structure. In this case, for example, the quadratic tree structure can be applied first and the binary tree structure and tertiary tree structure can be applied later. Alternatively, the binary tree structure / tertiary tree structure can be applied first. The coding procedure according to the present modality can be carried out on the basis of a final coding unit that is no longer divided. In this case, the largest coding unit can be used as the final coding unit based on the coding efficiency, or the like, depending on the figuration characteristics, or the coding unit can be recursively divided into coding units of a deeper depth. download as needed and a coding unit that is optimally sized can be used as the final coding unit. In this document, the coding procedure can include a procedure such as prediction, transform and reconstruction, which will be described later.

[039] In another example, the processing unit may include a coding unit (CU), a prediction unit (PU) or a transformer (TU). The coding unit can be divided from the largest coding unit (LCU) into coding units of a greater depth according to the quadratic tree structure. In this case, the largest coding unit can be directly used as the final coding unit based on the coding efficiency, or the like, depending on the figuration characteristics, or the coding unit can be recursively divided into coding units of a depth larger as needed and a coding unit that is optimally sized can be used as a final coding unit. When the smallest coding unit (SCU) is defined, the coding unit may not be divided into smaller coding units than the smallest coding unit. In this document, the final coding unit refers to a coding unit that is partitioned or divided into a prediction unit or a transformer. The prediction unit is a unit that is partitioned from an encoding unit, and can be a sample prediction unit. In the present document, the prediction unit can be divided into sub-blocks. The transformer can be divided from the coding unit according to the quadratic tree structure and can be a unit to derive a transform coefficient and / or a unit to derive a residual signal from the transform coefficient. Later in this document, the coding unit can be called a coding block (CB), the prediction unit can be called a prediction block (PB) and the transformer can be referred to as a transform block (TB) . The prediction block or prediction unit can refer to a specific area in the form of a block in a picture and include an array of prediction samples. Also, the transform or transformer block can refer to a specific area in the form of a block in a picture and include the transform coefficient or a matrix of residual samples.

[040] Predictor 110 can perform the prediction on a processing target block (henceforth, it can represent a current block or residual block), and can generate a predicted block including prediction samples from the current block. A prediction unit performed on predictor 110 can be a coding block, or it can be a transform block, or it can be a prediction block.

[041] Predictor 110 can determine whether intraprediction is applied or interpredition is applied to the current block. For example, predictor 110 can determine whether intraprediction or interpredition is applied to the CU unit.

[042] In the case of intraprediction, predictor 110 can derive a prediction sample from the current block based on a reference sample outside the current block in a figure to which the current block belongs (hereinafter, a current figure). In this case, the predictor 110 can derive the prediction sample based on an average or interpolation of neighboring reference samples from the current block (case (i)), or it can derive the prediction sample based on an existing reference sample in a specific direction (prediction) as to a prediction sample among the reference samples neighboring the current block (case (ii)). Case (i) can be called a non-directional or non-angular mode, and case (ii) can be called a directional or angular mode. In intraprediction, the prediction modes can include, as an example, 33 directional modes and at least two non-directional modes. Non-directional modes can include DC mode and planar mode. Predictor 110 can determine the application of the prediction mode to the current block using the prediction mode applied to the neighboring block.

[043] In the case of interpredition, predictor 110 can derive the prediction sample from the current block based on a sample specified by a motion vector in a reference figure. Predictor 110 can derive the prediction sample from the current block by applying any one of a jump mode, a blend mode and a motion vector prediction mode (MVP). In the case of jump mode and merge mode, predictor 110 can use motion information from the neighboring block as motion information from the current block. In the case of the jump mode, unlike the blend mode, a difference (residual) between the prediction sample and an original sample is not transmitted. In the case of MVP mode, a motion vector from the neighboring block is used as a motion vector predictor to derive a motion vector from the current block.

[044] In the case of interpretation, the neighboring block may include a spatial neighboring block existing in the current figure and a temporal neighboring block existing in the reference figure. The reference figure including the neighboring temporal block can also be called a colocalized figure (colPic). The movement information can include the movement vector and a reference figure index. Information such as prediction mode information and movement information can be encoded (entropy) and then output as a form of bit stream.

[045] When the movement information of a neighboring temporal block is used in the default mode and in the blend mode, a higher figure in a list of reference figures can be used as a reference figure. The reference figures included in the reference figures list can be aligned based on a difference in figure order count

(POC) between a current figure and a corresponding reference figure. A POC corresponds to a display order and can be broken down from a coding order.

[046] Subtractor 121 generates a residual sample which is a difference between an original sample and a prediction sample. If the default mode is applied, the residual sample may not be generated as described above.

[047] Transformer 122 transforms residual samples into units of a transform block to generate a transform coefficient. Transformer 122 can perform the transform based on the size of a corresponding transform block and a prediction mode applied to a coding block or prediction block spatially superimposed on the transform block. For example, residual samples can be transformed using a discrete sine transform (DST) transformation core if intraprediction is applied to the coding block or the prediction block overlaps the transform block and the transform block is a matrix residual 4x4 and is transformed using the discrete cosine transform (DCT) transformation core in other cases.

[048] Quantizer 123 can quantize transform coefficients to generate quantized transform coefficients.

[049] Rearranger 124 rearranges the quantized transform coefficients. The rearranger 124 can rearrange the quantized transform coefficients in the form of a block in a one-dimensional vector using a coefficient scanning method. Although rearranger 124 is described as a separate component, rearranger 124 can be part of quantizer 123.

[050] Entropy encoder 130 can perform entropy coding on the quantized transform coefficients. Entropy encoding may include an encoding method, for example, an exponential Golomb, a context-adaptable variable length encoding (CAVLC), a context-adaptive binary arithmetic encoding (CABAC), or the like. The entropy encoder 130 can perform the coding, according to an entropy coding, or according to a configured prediction method, together or separately from information (for example, a syntax element value or the like) necessary for the video reconstruction beyond quantized transform coefficients. Entropy-encoded information can be transmitted or stored in the unit of a network abstraction layer (NAL) in a bit stream form. The bit stream can be transmitted over a network or stored on digital storage media. In this document, the network may include a broadcasting network or a communications network, digital storage media may include various storage media, such as USB, SD, CD, DVD, Blu-ray, HDD, SDD, and so on. onwards.

[051] Decantant 125 decantifies values (transform coefficients) quantized by quantizer 123 and inverse transform 126 inversely transforms the values decanted by decantant 125 to generate a residual sample.

[052] Adder 140 adds a residual sample to a prediction sample to reconstruct a figuration. The residual sample can be added to the prediction sample in units of a block to generate a reconstructed block. Although adder 140 is described as a separate component, adder 140 can be part of predictor 110. However, adder 140 can be referred to as a reconstructed or reconstructed block generator.

[053] Filtto 150 can apply unlocking filtering and / or an adaptive displacement to the reconstructed figuration. The artifacts in a block outline in the reconstructed figuration or distortion in quantization can be corrected through unlock filtering and / or adaptive displacement to the sample. Adaptive displacement to the sample can be applied in units of a sample after the unlock filter is completed. Filter 150 can apply an adaptive loop filter (ALF) to the reconstructed figure. The ALF can be applied to the reconstructed figuration to which the sample filtering and / or adaptive displacement filtering was applied.

[054] Memory 160 can store a reconstructed picture (decoded picture) or information needed for encoding / decoding. In this document, the reconstructed figure can be the reconstructed figure filtered by filter 150. The stored reconstructed figure can be used as a reference figure for (inter) prediction of other figures. For example, memory 160 can store (reference) pictures used for interpretation. In this document, the figures used for interpretation may be designated according to a defined reference figure or a list of reference figures.

[055] Figure 2 briefly illustrates a structure of a video / image decoding device to which the present disclosure is applicable. Hereinafter, a video decoding apparatus may include an image decoding apparatus.

[056] Referring to Figure 2, a video decoding apparatus 200 may include an entropy decoder 210, a residual processor 220, a predictor 230, an adder 240, a filter 250 and a memory 260. The residual processor 220 may include a rearrangement 221, a decoder 222, an inverse transformer 223.

[057] Furthermore, although not described, the video decoding apparatus 200 may include a receiver for receiving a bit stream including video information. The receiver can be configured as a separate module or can be included in the entropy decoder 210.

[058] When a bit stream including video / image information is inserted, the video decoding device 200 can reconstruct a video / image / picture in association with a process by which video information is processed in the video encoding device .

[059] For example, the video decoding apparatus 200 can perform a video decoding using a processing unit applied to the video encoding apparatus. Thus, the video decoding processing unit block can be, for example, an encoding unit and, in another example, an encoding unit, a prediction unit or a transformer. The coding unit can be divided from the largest coding unit according to the quadratic tree structure and / or the binary tree structure and / or the tertiary tree structure.

[060] A prediction unit and a transformer can be additionally used in some cases, in which case the prediction block is a derived or partitioned block from the coding unit and can be a sample prediction unit. In the present document, the prediction unit can be divided into sub-blocks. The transformer can be divided from the coding unit according to the quadratic tree structure and can be a unit that derives a transform coefficient or a unit that derives a residual signal from the transform coefficient.

[061] The entropy decoder 210 can analyze the bit stream to output information necessary for video reconstruction or figuration reconstruction. For example, the entropy decoder 210 can decode information in the bit stream based on an encoding method such as exponential Golomb encoding, CAVLC, CABAC, or the like, and can output a value of a syntax element needed for video reconstruction and a quantized value of a transform coefficient referring to a residual.

[062] More specifically, a CABAC entropy decoding method can receive a bin corresponding to each syntax element in a bit stream, determine a context model using decoding target syntax element information and decoding information of neighboring destination blocks and decoding or information from a symbol / bin decoded in a previous step, predict the probability of bin generation according to the given context model and perform arithmetic decoding of the bin to generate a corresponding symbol for each syntax element value. In this document, the CABAC entropy decoding method can update the context model using information from a decoded symbol / bin to a context model of the next symbol / bin after determining the context model.

[063] Prediction information between the information decoded in the entropy decoder 210 can be provided to the predictor 250 and residual values, that is, quantized transform coefficients, in which the entropy decoding was performed by the entropy decoder 210 can be inserted in the 221 rearrangement.

[064] Rearranger 221 can rearrange the quantized transform coefficients into a two-dimensional block shape. The rearranger 221 can perform the rearrangement corresponding to the scan corresponding to that performed by the coding apparatus. Although rearranger 221 is described as a separate component, rearranger 221 can be part of deconverter 222.

[065] The decantant 222 can decantize the quantized transform coefficients based on a (de) quantization parameter to emit a transform coefficient. In this case, the information to derive a quantization parameter can be signaled from the coding device.

[066] Inverse transform 223 can inverse transform transform coefficients to derive residual samples.

[067] Predictor 230 can perform prediction on a current block, and can generate a predicted block including prediction samples from the current block. A prediction unit performed on predictor 230 can be a coding block or it can be a transform block or it can be a prediction block.

[068] Predictor 230 can determine whether to apply intraprediction or interpredition based on information about a prediction. In this case, a unit to determine which will be used between intraprediction and interpredition can be different from a unit to generate a prediction sample. In addition, a unit for generating the prediction sample can also be different in interpretation and intraprediction. For example, which will be applied between interpretation and intraprediction can be determined in CU units. Furthermore, for example, in the interpretation, the prediction sample can be generated by determining the prediction mode in PU unit, and in intraprediction, the prediction sample can be generated in TU unit by determining the prediction mode in PU unit.

[069] In the case of intraprediction, predictor 230 can derive a prediction sample from a current block based on a neighboring reference sample in a current figuration. Predictor 230 can derive the prediction sample from the current block by applying a directional mode or a non-directional mode based on the neighboring reference sample of the current block. In this case, a prediction mode that will be applied to the current block can be determined using an intraprediction mode of a neighboring block.

[070] In the case of interpretation, predictor 230 can derive a prediction sample from a current block based on a sample specified in a reference figure according to a motion vector. Predictor 230 can derive the prediction sample from the current block using one of the default mode, blending mode and MVP mode. In this document, the movement information necessary for interpreting the current block provided by the video coding apparatus, for example, a motion vector and information about a reference figure index can be acquired or derived based on the prediction information.

[071] In skip mode and merge mode, the movement information of a neighboring block can be used as movement information for the current block. In the present document, the neighboring block can include a spatial neighboring block and a temporal neighboring block.

[072] Predictor 230 can build a merge candidate list using motion information from available neighboring blocks and use information indicated by a merge index on the merge candidate list as a motion vector for the current block. The merge index can be signaled by the coding device. Motion information can include a motion vector and a reference figure. In default mode and in blend mode, a figuration ordered first in the list of reference figurations can be used as a reference figuration, when movement information from a neighboring temporal block is used.

[073] In the case of the omission mode, a (residual) difference between a prediction sample and an original sample is not transmitted, distinguished from the blending mode.

[074] In the case of MVP mode, the motion vector of the current block can be derived using a motion vector from a neighboring block as a motion vector predictor. In the present document, the neighboring block can include a spatial neighboring block and a temporal neighboring block.

[075] When blending mode is applied, for example, a list of candidates for blending can be generated using a motion vector from a reconstructed spatial neighboring block and / or a motion vector corresponding to a Col block which is a block temporal neighbor. A motion vector from a candidate block selected from the merge candidate list is used as the motion vector of the current block in the merge mode. The aforementioned prediction information may include a merge index indicating a candidate block that has the best motion vector selected from the candidate blocks included in the merge candidate list. In this document, predictor 230 can derive the motion vector from the current block using the Blending Index.

[076] When the MVP (Motion Vector Prediction) mode is applied as another example, a list of candidate motion vector predictors can be generated using a motion vector from a reconstructed neighboring space block and / or a motion vector. movement corresponding to a Col block which is a temporal neighbor block. That is, the motion vector of the reconstructed spatial neighbor block and / or the motion vector corresponding to the Col block which is the temporal neighbor block can be used as candidates for motion vector. The aforementioned information on prediction can include a prediction motion vector index indicating the best motion vector selected from among the motion vector candidates included in the list. In the present document, predictor 330 can select a prediction motion vector from the current block from the motion vector candidates included in the motion vector candidate list using the motion vector index. The coding device predictor can obtain a motion vector difference (MVD) between the motion vector of the current block and a motion vector predictor, encode the MVD and output the encoded MVD in the form of a bit stream. That is, the MVD can be obtained by subtracting the motion vector predictor from the motion vector of the current block. In the present document, the predictor 230 can acquire a motion vector included in the prediction information and derive the motion vector from the current block by adding the difference of motion vector to the motion vector predictor. In addition, the predictor can obtain or derive a reference figure index indicating a reference figure from the aforementioned prediction information.

[077] Adder 240 can add a residual sample to a prediction sample to reconstruct a current block or a current figuration. Adder 240 can reconstruct the current figure by adding the residual sample to the prediction sample in units of a block. When the default mode is applied, a residual is not transmitted and, thus, the prediction sample can become a reconstructed sample. Although adder 240 is described as a separate component, adder 240 can be part of predictor 230. However, adder 240 can be called a reconstructed or reconstructed block generator.

[078] Filtto 250 can apply unlocking filtering, adaptive displacement to the sample and / or ALF to the reconstructed figuration. In this document, the adaptive displacement to the sample can be applied in units of a sample after unlocking filtering. ALF can be applied after unlocking filtering and / or applying adaptive displacement to the sample.

[079] Memory 260 can store a reconstructed picture (decoded picture) or information needed for decoding. In this document, the reconstructed figure may be the reconstructed figure filtered by filter 250. For example, memory 260 may store figures used for interpretation. In this document, the figures used for interpretation may be designated according to a defined reference figure or a list of reference figures. A reconstructed figure can be used as a reference figure for other figures. The 360 memory can output reconstructed figures in an output order.

[080] However, as previously described, in performing a video encoding, a prediction is made to improve the compression efficiency. Through this, a predicted block including prediction samples for a current block as a block to be coded (that is, a target coding block) can be generated. In this document, the predicted block includes prediction samples in a spatial domain (or pixel domain). The predicted block is derived in the same way in a coding device and a decoding device, and the coding device can signal residual information (residual information) between the original block and the predicted block, instead of an original sample value. from an original block to the decoding device, thus increasing the image coding efficiency. The decoding apparatus can derive a residual block including residual samples based on residual information, add the residual block and the predicted block to generate reconstructed blocks including reconstructed samples, and generate a reconstructed figure including the reconstructed block.

[081] Residual information can be generated through a transformation and quantization procedure. For example, the coding apparatus can derive a residual block between the original block and the predicted block, perform a transformation procedure on residual samples (arrangement of residual samples) included in the residual block to derive transform coefficients, perform a quantization procedure in the transform coefficients to derive quantized transform coefficients, and signal residual information related to the decoding device (through a bit stream). In this document, residual information may include value information from the quantized transform coefficients, location information, a transform technique, a transform core, a quantization parameter, and the like. The decoding device can perform a reverse quantization / transform procedure based on residual information and derive residual samples (or residual blocks). The decoding device can generate a reconstructed figure based on the predicted block and the residual block. Likewise, for reference to the interpretation of a figuration later, the coding apparatus can also decantify / inversely transform the quantized transform coefficients to derive a residual block and generate a reconstructed figuration based on it.

[082] Figure 3 schematically illustrates a multiple transform technique according to the present disclosure.

[083] Referring to Figure 3, a transformer can correspond to the transformer on the aforementioned coding apparatus of Figure 1, and a reverse transformer can correspond to the aforementioned reverse transformer on the coding apparatus of Figure 1 or on the aforementioned reverse transformer on the decoding of Figure 2.

[084] The transformer can derive transform coefficients (primary) by performing a primary transform based on residual samples (residual sample arrangement) in the residual block (S310). In this document, the primary transform can include a multiple transform set (MTS). The multiple transform set can also be referred to as an adaptive multiple main transform in some cases.

[085] The adaptive multiple main transform can represent a method to perform a transform using additionally a Discrete Cosine Transform (DCT) type 2, a Discrete Sine Transform (DST) type 7, a DCT type 8, and / or an STD type 1. That is, the multiple principal transform can represent a transform method to transform a residual signal (or a residual block) in the spatial domain into transform coefficients (or primary transform coefficients) in the frequency domain based on a plurality of transform cores that are selected from DCT type 2, DST type 7, DCT type 8, and DST type 1. In this document, primary transform coefficients can be referred to as temporary transform coefficients from the point of view the transformer.

[086] That is, if the existing transform method is applied, the transformation from the spatial domain to the frequency domain for the residual signal (or the residual block) can be applied based on the type 2 DCT to generate the transform coefficients. On the other hand, if the adaptive multiple main transform is applied, the transform from the spatial domain to the frequency domain for the residual signal (or the residual block) can be applied based on DCT type 2, DST type 7, DCT type 8, and / or STD type 1 or similar, to generate the transform coefficients (or the primary transform coefficients). In this document, DCT type 2, DST type 7, DCT type 8, DST type 1, and the like, can be referred to as a transform type, a transform core, or a transform main.

[087] As a reference, the types of DCT / DST transform can be defined based on basic functions, and the basic functions can be represented as shown in the following table.

Table 1 Type of 2 T, 0, 1 ..., N-1 Transformed Base function 7/0): 1.70, 1, .... /; 2 ni Rj + D) T (D = ev: fon (E2G2D DCT-II 2 j = 0 where ww, = js = 1 iz0 =? 2 T (D = 0 "" "o * cos (==), DCT -V 2 2 where ww, = is i = 0 ,, = (is j = 0 1 i20 1 jz * 0 4 Tn: (2i + 1): (2j + 1) DCT-VII = l7— all TD = Gg1 aN + 2 a dis Tm (+11): (+19) pstl [mo = sn) .4 mn (2 +11): (+11) DSR-VII = ”L—— aa st = FTF sen (2N +1)

[088] If an adaptive multiple main transform is performed, a vertical transform core and a horizontal transform core for a target block from among the transform cores can be selected, and a vertical transform for the target block can be performed based on the vertical transform core, and a horizontal transform for the target block can be performed based on the horizontal transform core. In this document, the horizontal transform can represent a transform for horizontal components of the target block, and the vertical transform can represent a transform for vertical components of the target block. The vertical transform core / horizontal transform core can be adaptively determined based on a target block prediction mode (CU or sub-block) that covers the residual block and / or a transform index indicating a transform subset.

[089] The transformer can derive transform coefficients (secondary) by performing a secondary transform based on the transform coefficients (primary) (S320). If the primary transform is transformed from the spatial domain to the frequency domain, the secondary transform can be considered as the transform from the frequency domain. The secondary transform can include a non-separable transform. In that case, the secondary transform can be referred to as a non-separable secondary transform (NSST) or a mode-dependent non-separable secondary transform (MDNSST). The non-separable secondary transform can represent the transform that generates transform coefficients (or secondary transform coefficients) for the residual signal by secondarily transforming the (primary) transform coefficients derived through the primary transform based on a non-separable transform matrix. . In this document, the transform can be applied at once based on the non-separable transform matrix without separately applying the vertical transform and the horizontal transform (or applying the horizontal and vertical transform independently) to the transform coefficients (primary). That is, the non-separable secondary transform can represent the transform method that generates the transform coefficients (or the secondary transform coefficients) by transforming the vertical component and the horizontal component of the transform coefficients (primary) together without separating them. based on the non-separable transform matrix. The non-separable secondary transform can be applied to an upper left area of a block composed of transform coefficients (primary) (hereinafter, referred to as a transform coefficient block). For example, if both the width (W) and the length (H) of the transform coefficient block are 8 or more, a non-separable secondary transform 8x8 can be applied to the upper left 8x8 area of the transform coefficient block. In addition, if both the width (W) and the height (H) of the transform coefficient block are 4 or more and the width (W) or height (H) of the transform coefficient block is less than 8, a non-separable secondary transform 4x4 can be applied to an upper left area min (8, W) x min (8, H) of the transform coefficient block. However, an exemplary modality is not limited to this, and, for example, if only one condition in which the width (W) or height (H) of the transform coefficient block is less than 8 is satisfied, the secondary transform non-separable 4x4 can also be applied to the upper left area min (8, W) x min (8, H) of the transform coefficient block.

[090] Specifically, for example, when a 4x4 input block is used, NSST can be performed as follows.

[091] The 4x4 X input block can be represented as follows. [Equation 1] Xoo Xo1 Xo2 Xo3 X = X1o Xn X12 X13 X20 X21 X22 X23 X30 X31 X32 X33

[092] When X is expressed in a vector form, vector X can be represented as follows. [Equation 2] X = [Xoo Xo1 Xor Xoz Xio Xu Xiz Xi3z Xoo Xor Xoz Xog Xão Xar Xaão Xaal!

[093] In this case, NSST can be calculated as follows.

[Equation 3] F = T.X

[094] In this document, F denotes a vector transform coefficient and T denotes a 16x16 (non-separable) transform matrix.

[095] A vector of transform coefficient 16x1 É can be derived through Equation 3, and Ê can be reorganized as 4x4 blocks through a scanning order (horizontal, vertical, diagonal, etc.). However, the calculation described above is an example and a Hypercube-Givens transform (HyGT) or similar, can be used for the calculation of the secondary transform to reduce the complexity of NSST calculation.

[096] However, in NSST, a transform core (or transform number, type of transform) can be selected depending on mode. In this document, the method may include an intraprediction mode and / or an interpretive mode.

[097] As previously described, NSST can be performed based on the 8x8 transform or the 4x4 transform determined based on the width (W) and height (H) of the transform coefficient block. That is, NSST can be performed based on an 8x8 sub-block size or a 4x4 sub-block size. For example, in order to select the mode-based transform core, sets of three NSST cores can be configured for NSST for 8x8 sub-block size and 4x4 sub-block size. That is, 35 transform sets can be configured for the 8x8 subblock size, and 35 transform sets can be configured for the 4x4 subblock size. In that case, the 35 transform sets for the 8x8 sub-block size can include 3 transform cores 8x8, respectively, and in this case, the 35 transform sets for the 4x4 sub-block size can include 3 transform cores. 4x4. However, the size of the transform sub-block, the number of sets, and the number of transform cores in the set consist of an example and a different size of 8x8 or 4x4 can be used, or n sets can be configured and k cores of transform can be included in each set.

[098] The transform set can also be referred to as an NSST set, and the transform core in the NSST set can be referred to as an NSST core. The selection of a specific one among the transform sets can be carried out, for example, based on an intraprediction mode of a target block (CU or sub-block).

[099] For a reference, for example, the intraprediction mode can include two non-directional or non-angular intraprediction modes and 65 directional or angular intraprediction modes. Non-directional intraprediction modes can include a% 0 planar intraprediction mode and a DC H1 intraprediction mode, and directional intraprediction modes can include 65 H2 to 466 intraprediction modes. However, this is an example and the present disclosure can also be applied even when the number of intrapredict modes is different. However, the intraprediction mode ft 67 can still be used in some cases, and the intraprediction mode * 67 can represent a linear model (LM) mode.

[0100] Figure 4 shows, in an exemplary way, intradirectional modes of 65 prediction directions.

[0101] Referring to Figure 4, intraprediction modes having horizontal directionality and intraprediction modes having vertical directionality can be divided based on intraprediction mode f34 having an upper left diagonal prediction direction. H and V in Figure 3 refer to horizontal directionality and vertical directionality, respectively, and the numbers -32 to 32 indicate the displacement of 1/32 units in the sample grid position. The intraprediction modes ff2 to 433 have horizontal directionality, and the intraprediction modes H34 to 66 have vertical directionality. The tX18 intraprediction mode and the% 50 intraprediction mode represent a horizontal intraprediction mode and a vertical intraprediction mode, respectively. The intraprediction mode t2 can be referred to as a lower left diagonal intraprediction mode, the H34 intraprediction mode can be referred to as an upper left diagonal intraprediction mode, and the 466 intraprediction mode can be referred to as an upper diagonal intraprediction mode right.

[0102] In this case, the mapping between the 35 transform sets and the intrapredicting modes can be represented, for example, as shown in the following table. For reference, when the LM mode is applied to a target block, the secondary transform cannot be applied to the target block.

Table 2

ENTNONAOOOOOOORPEDOORDODODAZONORODONNCES [ira mass sa Jas [se [or [oo] 20] 0047] eaJ es [es [as 00 07 00 [29505 [se] so s4 [55] 50/57 so Jss [co [er [e2 [00 ex ] osJesr cm [sono fsefss [sa [o [eo [20 [20 [aro las [ee [es [ea erfeo robrol [rel ns [more rel ol [e] 7 [0 [5 [e [5 12 vovo]

[0103] However, when it is determined that a specific set is used, one of the k transform cores in the specific set can be selected using an NSST index. The encoding apparatus may derive an NSST index indicating a specific transform core based on a rate distortion (RD) check and may signal the NSST index to the decoding apparatus. The decoding device can select one of the k transform cores in the specific set based on the NSST index. For example, the NSST index value O can include a first NSST core, the NSST index value 1 can indicate a second NSST core, and the NSST index value 2 can indicate the third NSST core. Alternatively, the NSST index value O may indicate that the first NSST is not applied to the target block, and the NSST index values 1 to 3 may indicate the three transform cores.

[0104] Referring back to Figure 3, the transformer can perform the NSST based on the selected transform cores and obtain transform coefficients (secondary). The transform coefficients can be derived as transform coefficients quantized through the quantizer as described above, and encoded and signaled to the decoding apparatus and delivered to the reverse decoder / transformer in the encoding apparatus.

[0105] However, when the secondary transform is omitted as described above, transform (primary) coefficients, which are output from the primary (separable) transform, can be derived as quantized transform coefficients through the quantizer as described above and can be encoded and signaled to the decoding device and delivered to the reverse decoder / transformer on the encoding device.

[0106] The reverse transformer can perform a series of procedures in a reverse order of the procedure performed by the transformer described above. The reverse transformer can receive transform coefficients (inversely quantized), perform a secondary (inverse) transform to derive transform (primary) coefficients (S350), and perform a primary (inverse) transform on the transform (primary) coefficients to acquire a residual block (residual samples, In this document, the primary transform coefficients can be referred to as transform transform coefficients from the point of view of the reverse transformer. As previously described, the coding apparatus and the decoding apparatus may generate a block reconstructed based on the residual block and the predicted block and generate a reconstructed figuration based on the reconstructed block.

[0107] However, as previously described, when the secondary (inverse) transform is omitted, the transform coefficients (unquantified) can be received and the primary (separable) transform can be performed on them to acquire a residual block (residual samples) . As previously described, the coding apparatus and the decoding apparatus can generate a reconstructed block based on the residual block and the predicted block and generate a reconstructed figure based on the reconstructed block.

[0108] Figures 5A to 5C are diagrams to explain a reduced transform according to an exemplary embodiment of the present disclosure.

[0109] As previously described in Figure 3, in the non-separable secondary transform (hereinafter referred to as 'NSST'), block data of the transform coefficients obtained by applying the primary transform are divided into MxM blocks, and then an NSST MºxM? can be performed for each MxM block. M can be, for example, 4 or 8, but it is not limited to that.

[0110] NSST MºxM? it can also be applied in the form of a matrix product, but the Hypercube-Givens Transform (HyGT) described in Figure 3 can be used to calculate the NSST in order to decrease the computational amount and required memory capacity. HyGT is an orthogonal transform, and HyGT can include a rotation of Givens G ;, j (m, n) defined by an orthogonal matrix G (m, n, 8) as a basic component. The rotation of Givens G ;, j (m, n) can be expressed by Equation 4 below.

[Equation 4] sew, i = zsj = moui = j = n sen, i = mj = n, Gj (m, n) = = 09, i = nj = m 1, i = jeitmeizton, 0, otherwise.

[0111] The rotation of Givens based on Equation 4 can be illustrated in Figure 5A. Referring to Equation 4 and Figure 5A, it can be confirmed that one of the Givens rotations is described by only one angle (89).

[0112] Figure 5B illustrates an example of a round that constitutes a 16x16 NSST. More specifically, HYGT can be performed by combining Givens rotations in a hypercube arrangement, and the flow of the HyGT to 16 elements can be illustrated in the form of a butterfly as shown in Figure 5B. As illustrated in Figure 5B, a round is composed of 4 layers of Givens rotation, each layer of Givens rotation is composed of 8 Givens rotations, and each Givens rotation can be formed in a structure that selects 2 data from input as the connection configuration illustrated in Figure 5B to apply a rotation transform and then output the two input data transformed for rotation at the corresponding selection locations as they meet. NSST 16x16 can apply two rounds and a single permutation layer sequentially, and 16 data can be arbitrarily mixed through the corresponding permutation layer. All two rounds can be connected as shown in Figure 5B, but all Givens rotation layers for the two rounds can be different.

[0113] A 64x64 NSST consists of Givens rotation layers with 64 inputs and outputs, and the like, NSST 16x16, at least one round can be applied, and a round can be composed of 6 Givens rotation layers that are connected in a method similar to that of Figure 5B. As an example, the four rounds can be applied to NSST 64x64, and then a permutation layer can be applied to randomly mix 64 data. The rotation layers of Givens for each of the four rounds can be different from each other.

[0114] Figure 5B illustrates a round applied to a direct transform. When a reverse transform is applied, a reverse permutation layer is first applied, and then the corresponding Givens rotations can be applied along a direction from bottom to top in Figure 5B in order of the last round to the first round . An angle corresponding to each Givens rotation of the reverse NSST can be a value obtained by applying a sign - to the corresponding direct angle.

[0115] To enhance the coding efficiency, one or more rounds of HyGT can be used. As shown in Figure 5C, NSST can be composed of R rounds of HyGT, and can additionally include a classification pass. The classification pass can also be interpreted as an optional permutation pass, and can classify the transform coefficients based on the variance. As an example, HyGT two rounds can be applied to NSST 16x16, and HyGT four rounds can be applied to NSST 64x64.

[0116] Figure 6 is a diagram to explain a reduced transform according to an exemplary embodiment of the present disclosure.

[0117] In this specification, a “target block” can mean a current block or a residual block to be coded.

[0118] In this specification, a “reduced transform” can mean a transform that is performed for residual samples for the target block based on a transform matrix whose size is reduced according to a reduced factor. If the reduced transform is performed, the computational amount required for the transform can be reduced due to a reduction in the size of the transform matrix. That is, the reduced transform can be used to eliminate an issue of computational complexity that occurs when a large block is transformed or not separably transformed. The reduced transform can be referred to as a primary transform (or a main transform). The reduced transform can also be used for any type of transform, such as the primary transform (for example, DCT, DST, and the like) and the secondary transform (for example, NSST).

[0119] The reduced transform can be referred to by several terms, such as reduced transform, reduction transform, reduced transform, secondary reduced transform, reduction transform, simplified transform, simple transform, RTS, RST, or similar, and the names that can refer to the reduced transform are not limited to the examples listed.

[0120] In the reduced transform according to an exemplary modality, the reduced transform matrix can be determined by mapping a dimensional N vector to a dimensional R vector located in a different space, where R is less than N. N can mean a square of the length of one side of the block to be transformed or the total number of transform coefficients corresponding to the block to be transformed, and the reduced factor can mean an R / N value. The reduced factor can be referred to by several terms, such as a reduced factor, a reduction factor, a reduced factor, a reduction factor, a simplified factor, a simple factor, or the like. However, R can be referred to as a reduced coefficient, but in some cases, the reduced factor can also mean R. In addition, in some cases, the reduced factor can also mean an N / R value.

[0121] In an example mode, the reduced factor or reduced coefficient can be signaled through a bit stream, but the example mode is not limited to that. For example, a predetermined value for the reduced factor or reduced coefficient can be stored in each of the coding apparatus 100 and the decoding apparatus 200, in which case the reduced factor or reduced coefficient may not be signaled separately.

[0122] The size of the reduced transform matrix according to an exemplary modality is RxN smaller than the NxN size of the normal transform matrix, and can be defined as expressed in Equation 5 below.

[Equation 5] tu t2 ta tw Tennis shoes: 2 ta3, tri trr tra ** try

[0123] The matrix (T) in the reduced transform block illustrated in (a) of Figure 6 can mean the matrix (Trxn) of Equation 5. If the reduced transform matrix (Trxn) is multiplied by residual samples for the target block as illustrated in (a) of Figure 6, transform coefficients for the target block can be derived.

[0124] In an exemplary modality, if the block size to be transformed is 8x8, R = 16 (that is, R / N = 16/64 = 1/4), and the target block size is 64x64, the transformed reduced according to (a) of Figure 6 can be expressed by a matrix operation as in Equation 6 below.

[Equation 6] in ti2 tia. tie o. ti61 ti62 63 o tis a

[0125] In Equation 6, r1 the area can represent the residual samples for the target block. As a result of the operation of Equation 6, the transform coefficients (ci) for the target block can be derived, and the process of derivation of ci can be shown in Equation 7.

[Equation 7] paraide la R: c = 0 to jde 1a N: Cjr = ti * teC

[0126] As a result of the operation of Equation 7, the transform coefficients (c1 to cr) for the target block can be derived. That is, if R = 16.0s transform coefficients (c1 to c16) for the target block can be derived. If a regular transform is applied instead of the reduced transform and the transform matrix of 64x64 (NxN) in size is multiplied by a matrix including the residual samples of 64x1 (Nx1) in size, 64 (N) transform coefficients for the block target are derived, but since the reduced transform is applied, only 16 (R) transform coefficients for the target block are derived. The total number of transform coefficients for the target block is reduced from N to R and, therefore, the amount of data transmitted by the coding device 100 to the decoding device 200 can be reduced, thus enhancing the transmission efficiency between the encoding apparatus 100 and decoding apparatus 200.

[0127] By reviewing the size of the transform matrix, the size of the regular transform matrix is 64x64 (NxN), but the size of the reduced transform matrix is decreased by 16x64 (RxN), so that memory usage can be reduced by an R / N ratio when the reduced transform is performed compared to when the regular transform is performed. In addition, the number of multiplication operations can be reduced by an R / N ratio when the reduced transform matrix is used compared to the number of multiplication operations, NxXN, when the regular transform matrix is used.

[0128] In an exemplary embodiment, the transform coefficients for the target block can be derived by transforming the residual samples into the target block by transformer 122 of the coding apparatus 100; the transform coefficients for the target block can be transferred to the reverse transformer of the decoding apparatus 200; and the reverse transformer 223 of the decoding apparatus 200 can inversely transform the transform coefficients for the target block. Residual samples for the target block can be derived based on the reverse transform that is performed for the transform coefficients for the target block. That is, the detailed operations according to the inverse (reduced) transform are only in the opposite order to the detailed operations according to the (reduced) transform, and the detailed operations according to the reverse (reduced) transform and the detailed operations of according to the (reduced) transform are substantially similar.

[0129] The size of the reduced reverse transform matrix Tnxr according to an exemplary modality is NXR smaller than the size of the regular reverse transform matrix NxN, and the reduced reverse transform matrix TnxR has a transposition relationship with the transform matrix reduced TRrxn expressed in Equation 5.

[0130] The matrix T 'in the Reduced Inverse Transform block illustrated in (b) of Figure 6 can mean the reduced inverse transform matrix Tnxr. If the transform coefficients for the target block are multiplied by the reduced inverse transform matrix TnxR as illustrated in (b) of Figure 6, the primary transform coefficients for the target block or residual samples for the target block can be derived.

[0131] More specifically, if the reduced inverse transform is applied based on the secondary inverse transform, the primary transform coefficients for the target block can be derived when the transform coefficients are multiplied by the reduced reverse transform matrix TwxRr. On the other hand, if the reduced inverse transform is applied based on the primary inverse transform, the residual samples for the target block can be derived when the transform coefficients for the target block are multiplied by the reduced inverse transform matrix TR.

[0132] In an exemplary modality, if the block size to be inversely transformed is 8x8, R = 16 (that is, R / N = 16/64 = 1/4), and the target block size is 64x64, the reduced inverse transform according to (b) of Figure 6 can be expressed by a matrix operation as in Equation 8 below.

[Equation 8] ti1 ta 161 tz tz t161 [7 42 Es 61 [x [9 = * - SF ti6a cup + tisea

[0133] In Equation 8, ci to ci'ws can represent the transform coefficients for the target block. As a result of operating Equation 8, r; which represents the primary transform coefficients for the target block or the residual samples for the target block can be derived, and the derivation process of r; can be shown in Equation 9.

[Equation 9] for i de la N: n = 0 for jde 1a R: Tr + = titeo

[0134] As a result of the operation of Equation 9, laughs the rams that represent the primary transform coefficients for the target block or the residual samples for the target block can be derived. By reviewing the size of the reverse transform matrix, the size of the regular reverse transform matrix is 64x64 (NxN), but the size of the reduced reverse transform matrix is reduced by 64x16 (NxR), so that memory usage can be reduced by an R / N ratio when the reduced inverse transform is performed compared to when the regular inverse transform is performed. In addition, the number of multiplication operations can be reduced (NxR) to an R / N ratio when the reduced inverse transform matrix is used compared to the number of NxN multiplication operations when the regular inverse transform matrix is used.

[0135] Figure 7 is a flow chart that illustrates a reduced transform process according to an exemplary embodiment of the present disclosure.

[0136] Each step shown in Figure 7 can be performed by the decoding apparatus 200 shown in Figure 2. More specifically, S700 can be performed by the decoder 222 shown in Figure 2, and S710 and S720 can be performed by the reverse transformer 223 illustrated in Figure 2. Correspondingly, detailed descriptions that overlap with the contents mentioned in Figure 2 will be omitted or simplified.

[0137] In an exemplary modality, as previously described with reference to Figure 6, the detailed operations according to the (reduced) transform are only in the opposite order to the detailed operations according to the inverse (reduced) transform, and the detailed operations according to the (reduced) transform and the detailed operations according to the inverse (reduced) transform can be substantially similar. Correspondingly, those skilled in the art will readily understand that the descriptions from S700 to S720 for the reduced inverse transform described below can also be applied to the reduced transform in the same or similar way.

[0138] The decoding apparatus 200 according to an exemplary modality can derive transform coefficients by performing a decanting for quantized transform coefficients for a target block (S700).

[0139] The decoding apparatus 200 according to an exemplary mode can select a transform core (S710). More specifically, the decoder 200 can select the transform core based on at least a transform index, a width and height of an area to be transformed, an intraprediction mode used in image decoding, and information over a color component of the target block. However, the example mode is not limited to this, and, for example, the transform core is pre-defined, and no separate information for selecting the transform core can be signaled.

[0140] In one example, information about the color component of the target block can be signaled using Cldx. Cldx can indicate O if the target block is a luma block, and Cldx can indicate a non-zero value (for example, 1) if the target block is a chroma block, for example, a Cr block or a Cr block.

[0141] The decoding apparatus 200 according to an exemplary modality can apply the reduced inverse transform to the transform coefficients based on the selected transform core and a reduced factor (8720).

[0142] Figure 8 is a flowchart that illustrates a reduced transformation process according to another example of the present disclosure.

[0143] Each step shown in Figure 8 can be performed by the decoding apparatus 200 shown in Figure 2. More specifically, S800 can be performed by the decoder 222 shown in Figure 2, and S810 to S860 can be performed by the reverse transformer 223 illustrated in Figure 2. Correspondingly, detailed descriptions that overlap with the contents mentioned in Figure 2 will be omitted or simplified.

[0144] In an exemplary modality, as previously described with reference to Figure 6, the detailed operations according to the (reduced) transform are only in the opposite order for the detailed operations according to the inverse (reduced) transform, and the operations detailed according to the (reduced) transform and detailed operations according to the inverse (reduced) transform can be substantially similar. Correspondingly, those skilled in the art will readily understand that the descriptions from S800 to S860 for the reduced inverse transform described below can also be applied to the reduced transform in the same or similar way.

[0145] The decoding apparatus 200 according to an exemplary modality can perform a decanting for quantized coefficients for the target block (S800). If the transform is performed on the coding apparatus 100, the decoding apparatus 200 can derive the transform coefficients for the target block by disquantifying the quantized transform coefficients for the target block at S800. Conversely, if the transform is not performed on the coding apparatus 100, the decoding apparatus 200 may derive the residual samples for the target block by performing a decanting for quantized residual samples for the target block at S800.

[0146] The decoding apparatus 200 according to an exemplary embodiment can determine whether the transform was performed for the residual samples for the target block in the coding apparatus 100 (S810), and when it is determined that the transform was performed, the apparatus decoding number 200 can analyze the transformed index (or decoded from a bit stream) (S820). The transform index can include a horizontal transform index for a horizontal transform and a vertical transform index for a vertical transform.

[0147] In one example, the transform index can include a primary transform index, a main transform index, an NSST index, and the like. The transform index can be expressed as Transform idx, for example, and the NSST index can be expressed as NSST idx, for example. In addition, the horizontal transform index can be expressed as Transform idx h, and the vertical transform index can be expressed as Transform idx v.

[0148] The decoding apparatus 200 according to an exemplary modality may omit operations according to S820 to S860, when it is determined in S810 that the transform was not performed for the residual samples for the target block in the coding apparatus 100.

[0149] The decoding apparatus 200 according to an exemplary embodiment can select a transform core based on at least a transform index, a width and a height of an area to which the transform is applied, an intraprediction mode used in image decoding, and information about a color component of the target block (S830).

[0150] The decoding apparatus 200 according to an exemplary modality can determine if a condition to perform a reduced inverse transform for the transform coefficients for the target block is satisfied (S840).

[0151] In an example, if the width and height of the area to which the reduced inverse transform is applied are greater than a first coefficient, the decoder 200 can determine that the condition to perform the reduced reverse transform for the transform coefficients for the target block is satisfied.

[0152] In another example, if the product of the width and height of the area to which the reduced inverse transform is applied is greater than a second coefficient, and the smallest of the width and height of the area to which the reduced inverse transform is applied applied is greater than a third coefficient, the decoding apparatus 200 can determine that the condition to perform the reduced inverse transform for the transform coefficients for the target block is satisfied.

[0153] In yet another example, if the width and height of the area to which the reduced inverse transform is applied are less than or equal to a fourth coefficient, the decoder 200 can determine that the condition to perform the reduced inverse transform for the transform coefficients for the target block are satisfied.

[0154] In yet another example, if the product of the width and height of the area to which the reduced inverse transform is applied is less than or equal to a fifth coefficient and the smallest of the width and height of the area to which the inverse transform is applied. reduced is applied for less than or equal to a sixth coefficient, the decoding apparatus 200 can determine that the condition to carry out the reduced reverse transform for the transform coefficients for the target block is satisfied.

[0155] In yet another example, if at least one of the conditions in which the width and height of the area to which the reduced inverse transform is applied are greater than the first coefficient, the condition in which the product of width and height the area to which the reduced inverse transform is applied is greater than the second coefficient and the smallest of the width and height of the area to which the reduced inverse transform is applied is greater than the third coefficient, the condition in which the width and the height of the area to which the reduced inverse transform is applied are less than or equal to the fourth coefficient, and a condition in which the product of the width and height of the area to which the reduced inverse transform is applied is less than or equal to the fifth coefficient and the less than the width and height of the area to which the reduced inverse transform is applied is less than or equal to the sixth coefficient, the decoding device 200 can determine that the condition in which the reduced inverse transform is performed so the transform coefficients for the target block are satisfied.

[0156] In the examples above, the first to sixth coefficients can be any predetermined positive integer. For example, the first to sixth coefficients can be 4, 8, 16 or 32.

[0157] The inverse transform reduced according to an exemplary modality can be applied to a square area that is included in the target block

(that is, if the width and height of the area to which the reduced inverse transform is applied are equal), and in some cases, the width and height of the area to which the reduced inverse transform is applied can be set to values predetermined coefficients (for example, 4, 8, 16, 32, or similar). However, the area to which the reduced inverse transform is applied is not limited to the square area, and the reduced inverse transform can be applied to a rectangular area or a non-rectangular area. A more detailed description of the area to which the reduced inverse transform is applied will be described later with reference to Figure 10.

[0158] In one example, if the condition to perform the reduced inverse transform is met, it can be determined based on the transform index. That is, the transform index can indicate which transform was performed for the target block.

[0159] The decoding apparatus 200 according to an exemplary modality can perform the inverse (regular) transform for the transform coefficients for the target block when it is determined in S840 that the condition to perform the simplified inverse transform is not satisfied. As previously described with reference to Figure 3, the (reverse) transform can include, for example, DCT2, DCTA4, DCT5, DCT7, DCT8, DST1, DSTA4, DST7, NSST, JEM-NSST (HyGT), or the like, but not is limited to those.

[0160] The decoding apparatus 200 according to an exemplary modality can perform the reduced inverse transform for the transform coefficients for the target block when it is determined in S840 that the condition to perform the reduced inverse transform is satisfied (S860).

[0161] Figure 9 is a flow chart that illustrates a reduced transform process based on a non-separable secondary transform according to an exemplary embodiment of the present disclosure.

[0162] Each step shown in Figure 9 can be performed by the decoding apparatus 200 shown in Figure 2, and, more specifically, S900 can be performed by the decoder 222 shown in Figure 2, and S910 to S980 can be performed by the transformer inverse 223 illustrated in Figure 2. In addition, S900 in Figure 9 can correspond to S800 in Figure 8, S940 in Figure 9 can correspond to S830 in Figure 8, and S950 in Figure 9 can correspond to S840 in Figure 8. Correspondingly , detailed descriptions that overlap with the contents previously described with reference to Figures 2 and 8 will be omitted or simplified.

[0163] In an exemplary modality, as previously described with reference to Figure 6, the detailed operations according to the (reduced) transform are only in the opposite order to the detailed operations according to the inverse (reduced) transform, and the detailed operations according to the (reduced) transform and the detailed operations according to the inverse (reduced) transform can be substantially similar. Correspondingly, those skilled in the art will readily understand that the descriptions from S900 to S980 for the reduced inverse transform described below can also be applied to the reduced transform in the same or similar way.

[0164] The decoding apparatus 200 according to an exemplary modality can perform a decanting for the quantized coefficients for the target block (S900).

[0165] The decoding apparatus 200 according to an exemplary embodiment can determine whether the NSST was performed for the residual samples for the target block in the coding apparatus 100 (S910), and when it is determined that the NSST was performed, the apparatus decoding 200 can analyze the NSST index (or decoded from the bit stream) (S920).

[0166] The decoder 200 according to an exemplifying mode can determine whether the NSST index is greater than O (S930), and when it is determined that the NSST index is greater than O, the decoder 200 can select the transformed core based on at least one of the

NSST index, a width and height of an area to which the NSST index is applied, an intraprediction mode, and information about a color component of the target block (S940).

[0167] The decoding apparatus 200 according to an exemplary modality can determine whether the condition to carry out the reduced reverse transform for the transform coefficients for the target block is satisfied (S950).

[0168] The decoding apparatus 200 according to an exemplary modality can perform the inverse (regular) transform without relying on the reduced inverse transform for the transform coefficients for the target block, if it is determined in S950 that the condition to perform the reduced inverse transform is not satisfied.

[0169] The decoding apparatus 200 according to an exemplary modality can perform an inverse NSST based on the reduced inverse transform for the transform coefficients for the target block, if it is determined in S950 that the condition for performing the reduced reverse transform is satisfied.

[0170] The decoding apparatus 200 according to an exemplary modality may omit operations according to S920 to S970 if it is determined in S910 that NSST was not performed for the residual samples for the target block in the coding apparatus 100.

[0171] The decoding apparatus 200 according to an exemplary modality may omit operations according to S940 to S970, if it is determined in S930 that the NSST index is not greater than O.

[0172] The decoding apparatus 200 according to an exemplary embodiment can perform a primary reverse transform for primary transform coefficients for the derived target block by applying the inverse NSST. When the primary reverse transform is performed for the primary transform coefficients, residual samples for the target block can be derived.

[0173] Figure 10 is a block diagram that illustrates a block to which the reduced transform is applied according to an exemplary embodiment of the present disclosure.

[0174] As described above with reference to Figure 8, the area to which the reduced (inverse) transform is applied to the target block is not limited to the square area, and the reduced transform can be applied to the rectangular area or the non-rectangular area.

[0175] Figure 10 illustrates an example in which the reduced transform is applied to a non-rectangular area in a target block 1000 having 16x16 in size. Ten blocks 1010 hatched in Figure 10 represent areas where the reduced transform is applied to target block 1000. Since the sizes of the respective minimum unit blocks are 4x4, the reduced transform is applied to 10 4x4 pixels (that is, the reduced transform is applied at 160 pixels) according to the example in Figure 10. When R = 16, the size of the reduced transform matrix can be 16x160.

[0176] However, those skilled in the art can readily understand that the arrangement of the minimum unit blocks 1010 included in the area to which the reduced transform shown in Figure 10 is applied consists of only one of a large number of examples. For example, the minimum unit blocks included in the area to which the reduced transform is applied cannot be adjacent to each other, or they can have a relationship sharing only one vertex between them.

[0177] Figure 11 is a flow chart that illustrates an operation of a video encoding device according to an exemplary embodiment of the present disclosure.

[0178] Each step shown in Figure 11 can be performed by the coding apparatus 100 shown in Figure 1. More specifically, S1100 can be performed by subtractor 121 shown in Figure 1, S1110 can be performed by transformer 122 shown in Figure 1 , S1120 can be performed by the quantizer 123 shown in Figure 1, and S1130 can be performed by the entropy encoder 130 shown in Figure 1. In addition, the operations according to S1100 to S1130 are based on some of the contents described above with reference to Figures 6 to 10. Correspondingly, detailed descriptions that overlap with the contents previously described with reference to Figures 1 and 6 to 10 will be omitted or simplified.

[0179] The coding apparatus 100 according to an exemplary embodiment can derive residual samples for the target block (S1100).

[0180] The coding apparatus 100 according to an exemplary modality can derive transform coefficients for a target block based on the reduced transform for the residual samples (S1110). In one example, the reduced transform can be performed based on a reduced transform matrix, and the reduced transform matrix can be a non-square matrix whose number of rows is less than the number of columns.

[0181] In an exemplifying embodiment, S1110 can include determining whether a condition to apply the reduced transform is satisfied, generating and encoding a transform index based on the determination, selecting a transform core, and applying the reduced transform to residual samples with based on the selected transform core and a reduced factor, when the condition to apply the reduced transform is satisfied. At that time, the size of the reduced transform matrix can be determined based on the reduced factor.

[0182] If the reduced transform according to S1110 is based on a primary transform, primary transform coefficients for the target block can be derived when the reduced transform is performed for the residual samples for the target block. The decoding apparatus 200 can perform an NSST for the primary transform coefficients for the target block, and at that time, NSST can be performed on the basis of the reduced transform or performed without being based on the reduced transform. When NSST is performed based on the reduced transform, this may correspond to the operation according to S1110.

[0183] The coding apparatus 100 according to an exemplary embodiment can derive quantized transform coefficients by performing a quantization based on the transform coefficients for the target block S1120.

[0184] The coding apparatus 100 according to an exemplary embodiment can encode information about the quantized transform coefficients (S1130). More specifically, the coding apparatus 100 can generate information about the quantized transform coefficients and encode information about the generated quantized transform coefficients. Information about the quantized transform coefficients can include residual information.

[0185] In one example, information about quantized transform coefficients can include at least one of the information about whether the reduced transform is applied, information about the reduced factor, information about a minimum transform size to which the reduced transform is applied. , and information about a maximum transform size to which the reduced transform is applied. A more detailed description of the information about the quantized transform coefficients will be described later in Figure 12.

[0186] Referring to S1110, it can be confirmed that the transform coefficients for the target block are derived based on the reduced transform for the residual samples. By reviewing the size of the transform matrix, the size of the regular transform matrix is NxN, but the size of the reduced transform matrix is decreased by RxN, so that memory usage can be decreased by an R / N ratio when the reduced transform is performed compared to when the regular transform is performed. In addition, the number of multiplication operations can be reduced (RxN) to an R / N ratio when the reduced transform matrix is used compared to the number of NxXN multiplication operations when the regular transform matrix is used. In addition, since only the R transform coefficients are derived when the reduced transform is applied, the total number of transform coefficients for the target block is reduced from N to R compared to a case where the N transform coefficients are derived when the regular transform is applied, so that the amount of data transmitted by the encoding apparatus 100 to the decoding apparatus 200 can be reduced. In short, it is possible to enhance the transform efficiency and the coding efficiency of the coding apparatus 100 through the reduced transform according to S1110.

[0187] Figure 12 is a flow chart illustrating an operation of a video decoding device according to an exemplary embodiment of the present disclosure.

[0188] Each shown in Figure 12 can be performed by the decoder 200 shown in Figure 2. More specifically, S1200 can be performed by the entropy decoder 210 shown in Figure 2, S1210 can be performed by the decoder 222 illustrated in Figure 2, S1220 can be performed by the reverse transformer 223 shown in Figure 2, and S1230 can be performed by the adder 240 shown in Figure 2. In addition, the operations according to S1200 to S1230 are based on some of the contents previously described with reference to Figures 6 to 10. Correspondingly, detailed descriptions that overlap with the contents previously described with reference to Figures 2 and 6 a will be omitted or simplified.

[0189] The decoding apparatus 200 according to an exemplary embodiment can derive quantized transform coefficients for the target block from the bit stream (S1200). More specifically, the decoding apparatus 200 can decode information about the quantized transform coefficients for the target block from the bit stream, and derive the quantized transform coefficients for the target block based on information about the transform coefficients quantized for the target block. Information about the quantized transform coefficients for the target block can be included in a set of sequence parameters (SPS) or a slice header, and can include at least one of the information about whether the reduced transform is applied, information about the reduced factor, information about the minimum transform size to which the reduced transform is applied, information about the maximum transform size to which the reduced transform is applied, and information about the size of the reduced inverse transform.

[0190] More specifically, information on whether the reduced transform is applied can be represented by an enabled indicator, information on the reduced factor can be represented by a reduced factor value, information on the minimum transform size when which the reduced inverse transform is applied are represented by a minimum transform size value, information about the maximum transform size to which the reduced inverse transform is applied can be represented by the maximum transform size value, and information about the reduced reverse transform size can be represented by a reduced reverse transform size value. At that time, the enabled indicator can be signaled via a first syntax element, the reduced factor value can be signaled via a second syntax element, the minimum transform size value can be signaled via a third syntax element , and the maximum transform size value can be signaled via a fourth syntax element, and the reduced inverse transform size value can be signaled via a fifth syntax element.

[0191] In an example, the first syntax element can be expressed as the Reduced transform enabled flag syntax element. The Reduced transform enabled flag syntax element can indicate 1 if the reduced transform is applied, and the Reduced transform enabled flag syntax element can indicate O if the reduced transform is not applied. If the Reduced transform enabled flag syntax element is not flagged, a syntax element value

Reduced transform enabled flag can be estimated to be 0.

[0192] In addition, the second syntax element can be expressed as a Reduced transform factor syntax element. The Reduced transform factor syntax element can indicate an R / N value, where N can mean the square of the length of one side of the block to which the transform is applied or the total number of transform coefficients corresponding to the block to which the transform is applied. is applied. R can mean a reduced coefficient less than N. However, the example is not limited to that, and, for example, Reduced transform factor can also indicate R instead of R / N. Revising for the reduced reverse transform matrix, R means the number of columns of the reduced reverse transform matrix, and N means the number of rows of the reduced reverse transform matrix, and at that time, the number of columns in the reduced reverse transform matrix must be less than the number of rows. R can be, for example, 8, 16, 32, or the like, but is not limited to that. If the Reduced transform factor syntax element is not signaled, the value of Reduced transform factor can be estimated as R / N (or R).

[0193] In addition, the third syntax element can be expressed as a min reduced transform size syntax element. If the min reduced transform size syntax element is not flagged, the min reduced transform size value can be estimated as 0.

[0194] In addition, the fourth syntax element can be expressed as a max reduced transform size syntax element. If the max reduced transform size syntax element is not flagged, a max reduced transform size value can be estimated as O.

[0195] In addition, the fifth syntax element can be expressed as a reduced transform size syntax element. The size of the reduced inverse transform included and signaled in the reduced transform size syntax element can indicate the size of the area to which the reduced inverse transform is applied or the size of the reduced transform matrix, but is not limited to that. If the reduced transform size syntax element is not flagged, the value of reduced transform size can be estimated as 0.

[0196] Table 3 below shows an example in which information about the quantized transform coefficients for the target block is included and signaled in the SPS. Table 3 [sec parameter set | pesenmter] ua) sps max sub layers minus1 [profa see teveltps max sub layers mins) sps seq parameter set id chroma format idc | inehvoma fomatiaes = a) - | separate color plane flag pic width in luma samples conformance window flag if (conformance window flag) (| | conf win right offeset conf win top offset conf win bottom offset ae Reduced transform enabled flag Ifíreduced transform enabled flag) (| reduced transform enabled flag) (min reduced tansform size max reduced transform size

+) sps extension flag if (sps extension flag) while (more rbsp data ()) | | [resp rata ts of E j | Lo

[0197] The decoding apparatus 200 according to an exemplary modality can derive transform coefficients by performing a decanting for the quantized transform coefficients for the target block (81210).

[0198] The decoding apparatus 200 according to an exemplary embodiment can derive residual samples for the target block based on the reduced inverse transform for the transform coefficients (S1220). In one example, the reduced inverse transform can be performed based on the reduced reverse transform matrix, and the reduced reverse transform matrix can be a non-square matrix whose number of columns is less than the number of rows.

[0199] In an exemplary embodiment, S1220 may include decoding a transform index, determining whether a condition to apply the reduced inverse transform is satisfied based on the transform index, selecting a transform core, and applying the reduced inverse transform to the transform coefficient based on the selected transform core and a reduced factor, when the condition to apply the reduced inverse transform is satisfied. At that time, the size of the reduced inverse transform matrix can be determined based on the reduced factor.

[0200] If the reduced inverse transform according to S1220 is based on the inverse NSST, the primary transform coefficients for the target block can be derived when the reduced reverse transform is performed for the transform coefficients for the target block. The decoding apparatus 200 can perform the primary reverse transform for the primary transform coefficients for the target block, and at that time, the primary reverse transform can be performed based on the reduced reverse transform or performed without being based on the reduced reverse transform.

[0201] Alternatively, when the reduced inverse transform according to S1220 is based on the primary reverse transform, residual samples for the target block can be directly derived by performing the reduced reverse transform for the transform coefficients for the target block.

[0202] The decoding apparatus 200 according to an exemplary embodiment can generate a reconstructed figure based on residual samples for the target block and prediction samples for the target block (S1230).

[0203] Referring to S1220, it can be confirmed that the residual samples for the target block are derived based on the reduced inverse transform for the transform coefficients for the target block. By reviewing the size of the inverse transform matrix, the size of the regular inverse transform matrix is NxN, but the size of the reduced inverse transform matrix is reduced to NxR, so that memory usage can be reduced by an R ratio / N when the reduced transform is performed compared to when the regular transform is performed. In addition, the number of multiplication operations can be reduced (NxR) to an R / N ratio when the reduced inverse transform matrix is used compared to the number of NXN multiplication operations when the regular inverse transform matrix is used. In addition, since only the R transform coefficients need to be decoded when the reduced inverse transform is applied, the total number of transform coefficients for the target block can be N to R when compared to a case where the N transform coefficients need be decoded when the regular inverse transform is applied, thus enhancing the decoding efficiency. In short, it is possible to enhance the transform efficiency (inverse) and the coding efficiency of the decoding apparatus 200 through the reduced reverse transform according to S1220.

[0204] The internal components of the aforementioned device may be processors that execute consecutive processes stored in memory, or they may be hardware components composed of other hardware. These can be located inside / outside the device.

[0205] The modules mentioned above can be omitted or replaced by other modules that perform the same / similar operations according to the example modalities.

[0206] The aforementioned method according to the present disclosure can be implemented in the form of software, and the coding apparatus and / or the decoding apparatus according to the present disclosure can be included in the apparatus which performs image processing such as a TV, a computer, a smartphone, a set-top box, a display device, or the like.

[0207] In the exemplary modalities mentioned above, although the methods are described based on flowcharts shown as a series of steps or blocks, the present disclosure is not limited to the order of the steps, and a given step can occur in a different order or simultaneously to a different step from the one previously described. In addition, individuals skilled in the art will understand that the steps in the flowchart are not exclusive, and other steps can be included or one or more steps in the flowcharts can be excluded without affecting the scope of the present disclosure.

[0208] When the modalities of the present disclosure are implemented in software, the method described above can be implemented by modules (processes, functions, and so on) that perform the functions described above. These modules can be stored in memory and run by a processor.

The memory can be internal or external to the processor, and the memory can be coupled to the processor using various notorious means.

The processor may comprise an application specific integrated circuit (ASIC), other chip sets, a logic circuit and / or a data processing device.

The memory can include a ROM (read-only memory), a RAM (random access memory), a flash memory, a memory card, a storage medium and / or other storage device.

Claims (15)

1. Image decoding method performed by a decoding device, the method being CHARACTERIZED by the fact that it comprises: deriving quantized transform coefficients for a target block from a bit stream; derive transform coefficients by performing decanting for the quantized transform coefficients for the target block; derive residual samples for the target block based on reduced inverse transform for the transform coefficients; and generate a reconstructed figure based on the residual samples for the target block and prediction samples for the target block, in which the reduced inverse transform is performed based on a reduced reverse transform matrix, in which the reduced reverse transform matrix is a non-square matrix, the number of columns in the non-square matrix being less than the number of rows in the non-square matrix. 2. Method, according to claim 1, CHARACTERIZED by the fact that the derivation of residual samples for the target block based on the reduced inverse transform comprises: decoding a transform index; determine whether a condition to apply the reduced inverse transform is reduced, based on the transform index; select a transform core; and when the condition to apply the reduced inverse transform is satisfied, apply the reduced inverse transform to the transform coefficients based on the selected transform core and a reduction factor, in which a size of the reduced reverse transform matrix is determined based on reduction factor. 3. Method, according to claim 2, CHARACTERIZED by the fact that the transform core is selected based on at least one of the transform index, a width and a height of an area to which the reduced inverse transform is applied , an intrapredictive mode used for image decoding and information about a color component of the target block. 4. Method, according to claim 2, CHARACTERIZED by the fact that the condition to apply the reduced inverse transform comprises at least one of a condition in which a width and height of an area to which the reduced inverse transform is applied are greater than a first coefficient, a condition in which the product of the width and height to the area to which the reduced inverse transform is applied is greater than a second coefficient and less than one of the width and height of the area to which the inverse transform is applied. reduced is applied is greater than a third coefficient, a condition in which the width and height of the area to which the reduced inverse transform is applied are less than or equal to a fourth coefficient, and a condition in which the product of the width and height the area to which the reduced inverse transform is applied is less than or equal to a fifth coefficient and less than the width and height of the area to which the reduced inverse transform is applied is less or equal to a sixth coefficient. 5. Method, according to claim 1, CHARACTERIZED by the fact that the width and height of an area to which the reduced inverse transform is applied to the target block are equal. 6. Method, according to claim 1, CHARACTERIZED by the fact that the reduced inverse transform is performed based on a secondary transform, and in which the area to which the secondary transform is applied in the target block has a non-rectangular shape. 7. Method, according to claim 1, CHARACTERIZED by the fact that a set of sequence parameters (SPS) or a slice header comprised in the bit stream comprises at least one among the information about whether the reduced inverse transform is applied , information about the reduced factor, information about a minimum transform size to which the reduced inverse transform is applied, information about a maximum transform size to which the reduced inverse transform is applied, and information about the reduced inverse transform size. 8. Method, according to claim 7, CHARACTERIZED by the fact that the SPS or the slice header comprised in the bit stream comprises at least one of an enabled indicator that represents the information about whether the reduced inverse transform is applied, a reduced factor value that represents the information about the reduced factor, a value of the minimum transform size that represents the information about the minimum transform size to which the reduced inverse transform is applied, a value of the maximum transform size that represents the information about the maximum transform size to which the reduced inverse transform is applied, and a size value of the reduced inverse transform, and where the enabled indicator is signaled through a first syntax element, the reduced factor value is itself through a second syntax element, the minimum transform size value is signaled through a third syntax element, the maximum transform size value is signaled through a fourth syntax element, and the reduced inverse transform size value is signaled through a fifth syntax element. 9. Image coding method performed by a coding device, the method being CHARACTERIZED by the fact that it comprises: deriving residual samples for a target block; derive transform coefficients for the target block based on the reduced transform for the residual samples; derive quantized transform coefficients by applying quantization based on the transform coefficients for the target block; and encode information about the quantized transform coefficients, where the reduced transform is performed based on a reduced transform matrix, where the reduced transform matrix is a non-square matrix, the number of rows of the non-square matrix being less than the number of columns in the non-square matrix. 10. Method, according to claim 9, CHARACTERIZED by the fact that the derivation of the transform coefficients for the target block based on the reduced transform comprises: determining whether a condition to apply the reduced transform is satisfied; generate and code a transform index based on the determination; select a transform core; and applying the reduced transform to the residual samples based on the selected transform core and a reduced factor, when the condition to apply the reduced transform is satisfied, in which a size of the reduced transform matrix is determined based on the reduced factor. 11. Method, according to claim 10, CHARACTERIZED by the fact that the transform core is selected based on at least the transform index, a width and a height of an area to which the reduced transform is applied, a intrapredition used for image encoding, and information about a color component of the target block. 12. Method, according to claim 10, CHARACTERIZED by the fact that the condition to apply the reduced transform comprises at least one among a condition in which the width and height of an area to which the reduced transform is applied are greater than a first coefficient, a condition in which the product of the width and height to the area to which the reduced transform is applied is greater than a second coefficient and less than one of the width and height of the area to which the reduced transform is applied is greater than a third coefficient, a condition in which the width and height of the area to which the reduced transform is applied are less than or equal to a fourth coefficient, and a condition in which the product of the width and height of the area to which the reduced transform is applied is less than or equal to a fifth coefficient and less than the width and height of the area to which the reduced transform is applied is less than or equal to a sixth coefficient. 13. Method, according to claim 9, CHARACTERIZED by the fact that the reduced transform is performed based on the secondary transform of the area to which the secondary transform is applied in the target block has a non-rectangular shape. 14. Method, according to claim 9, CHARACTERIZED by the fact that the information on the quantized transform coefficients comprises at least one among the information about whether the reduced transform is applied, information about the reduced factor, information about a minimum size of transform to which the reduced transform is applied, information about a maximum transform size to which the reduced transform is applied, and information about the reduced transform size. 15. Decoding device to perform image decoding, FEATURED by the fact that it comprises: an entropy decoder that derives quantized transform coefficients for a target block from a bit stream; a decantant that derives transform coefficients by performing a decantantization for the quantized transform coefficients for the target block; an inverse transformer that derives residual samples for the target block based on the reduced inverse transform for the transform coefficients; and an adder that generates a reconstructed figure based on residual samples for the target block and prediction samples for the target block, where the reduced inverse transform is performed based on a reduced inverse transform matrix, and the reduced inverse transform matrix is a non-square matrix, the number of rows in the non-square matrix being less than the number of columns in the matrix not square.